Relaxing Hicks-Leontief price aggregation by allowing overlapping groups of goods

The Hicks-Leontief composite commodity theorem permits aggregation of sets of goods that have identical price movements into composite groups of goods, each of which can be treated like a single good for demand analysis. Here Hicks-Leontief is generalized by permitting composite commodities to overlap, that ss, the same good is allowed to appear in more than one group. This generalization permits aggregation for arbitrary preferences with dramatically weaker restrictions on relative price movements than Hicks-Leontief.